"The Converse Theorem of the Pythagorean Theorem" PPT courseware

Description

"The Converse Theorem of the Pythagorean Theorem" PPT courseware

Review the past and learn the new

1. State the Pythagorean Theorem in written language.

The sum of the squares of the two right-angled sides of a right triangle is equal to the square of the hypotenuse.

2. State its converse proposition and determine whether its converse proposition is true or false?

If the sum of the squares of two sides of a triangle is equal to the square of the third side, then the triangle is a right triangle.

Explore the converse of the Pythagorean Theorem

It is said that the ancient Egyptians once used the following method to draw right angles: tie a long rope with 13 equally spaced knots, and then use the length of 3 knots, 4 knots, and 5 knots as the side length, and nail it with wooden stakes. A triangle, they think one of the angles is a right angle. Do you know why?

learning target:

(1) Explore and prove the converse theorem of the Pythagorean Theorem.

(2) Be able to use the converse theorem of the Pythagorean theorem to determine whether a triangle with known three-side lengths is a right-angled triangle.

(3) Be able to flexibly apply the Pythagorean theorem and its inverse to understand comprehensive questions.

(4) Understand the concept of the Pythagorean array and be able to give examples of what kind of three numbers are the Pythagorean array.

(5) Understand the idea of ​​combining numbers and shapes.

Self-study guide one

Carefully read the content above in Example 2 on pages 56 to 58 of the textbook:

1. Understand the general proof of the converse theorem of the Pythagorean theorem.

2. When looking at Example 1, pay attention to summarizing the steps to solve the example problem.

After 6 minutes, compare who can imitate the examples and do the exercises correctly.

Is the triangle below with sides a, b, and c a right triangle? If so then which angle is a right angle?

(1)a=25, b=20, c=15____ _____;

(2)a=13, b=14, c=15____ _____;

(3)a=1, b=2, c=√3 ____ _____;

(4)a:b: c=3:4:5 _____ _____ ;

The converse of the Pythagorean theorem

If the sum of the squares of two sides of a triangle is equal to the square of the third side, then the triangle is a right triangle.

∵a2+b2=c2

∴ΔABC is a right triangle

induction:

How to determine a right triangle:

1. Definition (angle): A triangle with one right angle is a right triangle.

2. The converse theorem of the Pythagorean theorem (sides): If the lengths of the three sides a, b, and c of a triangle (c is the largest side) satisfy a2+b2=c2, then the triangle is a right triangle.

Self-study test 2

1. If line segments a, b, c can form a right triangle, their ratio may be ( )

A. 3:4:7; B. 5:12:13; C. 1:2:4; D. 1:3:5.

2. If the lengths of the three sides of a right triangle are expanded by the same multiple, the resulting triangle is ( )

A. It is a right triangle; B. It may be an acute triangle;

C. It may be an obtuse triangle; D. It cannot be a right triangle.

3. The three sides of the triangle are a, b, c, and satisfy the equation (a+b)2-c2=2ab, then the triangle is: ( )

A. A right triangle; B. An acute triangle;

C. is an obtuse triangle; D. is an isosceles right triangle.

summary

1. Through the study of this lesson, do you know that when the three sides of a triangle satisfy what relationship in quantity, this triangle is a right triangle?

2. Please summarize, what are the methods to determine whether a triangle is a right triangle?

The converse of the Pythagorean theorem

If the lengths of the three sides a, b, and c of a triangle satisfy a2 + b2 = c2, then the triangle is a right triangle.

The three positive integers satisfying a2 + b2 = c2 are called Pythagorean numbers.

In ΔABC, a, b, c are the lengths of the three sides, among which c is the largest side,

If a2 +b2=c2, then ΔABC is a right triangle;

If a2 +b2>c2, then ΔABC is an acute triangle;

If a2 +b2

Keywords: teaching courseware for the converse theorem of the Pythagorean theorem, Qingdao edition eighth grade mathematics volume PPT courseware download, eighth grade mathematics slide courseware download, download PPT courseware for the converse theorem of the Pythagorean theorem, .PPT format;

For more information about the "Converse Theorem of the Pythagorean Theorem" PPT courseware, please click on the "Converse Theorem of the Pythagorean Theorem" ppt tag.

"The Converse Theorem of the Pythagorean Theorem" PPT courseware 3:

"The Converse Theorem of the Pythagorean Theorem" PPT courseware 3 1. Knowledge connection: Question 1. Can you tell what are the characteristics of a right triangle? (1) One angle is a right angle: (2) The right-angled side of 30 degrees is equal to the slope Half of the side; (3) Pythagorean Theorem: The sum of the squares of two right-angled sides is equal to the hypotenuse..

"The Converse Theorem of the Pythagorean Theorem" PPT courseware 2:

"The Converse Theorem of the Pythagorean Theorem" PPT Courseware 2 Review the past and learn the new 1. Explain the Pythagorean Theorem in written language. The sum of the squares of the two right-angled sides of a right triangle is equal to the square of the hypotenuse. 2. State its converse proposition and determine whether its converse proposition is true or false? if..

"The Converse Theorem of the Pythagorean Theorem" PPT Courseware 5 of the Pythagorean Theorem:

"The Converse Theorem of the Pythagorean Theorem" Pythagorean Theorem PPT courseware 5 Learning objectives: 1. Understand the converse theorem of the Pythagorean theorem, go through the theorem exploration process of observation-measurement-conjecture-demonstration, and experience the basic idea of ​​proving mathematical propositions by construction; 2. Understand the concept of converse proposition...

File Info

Update Time: 2024-07-01

This template belongs to Mathematics courseware Qingdao Edition Eighth Grade Mathematics Volume 2 industry PPT template

Preview